The old lady in the picture on Oliver Bacon's mantelpiece is his late mother. Oliver, who had begun life "in a filthy little alley" seems to crave his late mother's approval, which we see by the fact that he stands beneath the portrait and talks to it, telling his mother's image about the successes that he enjoys.
At the end of the story, Oliver speaks to his mother again, begging her forgiveness. At this moment, the reader is told that he feels as though he were "the little boy in the alley" all over again, which is indicative of just how much his mother's approval meant to him.
These conversations with his mother, and his ongoing desire for her approval, imply that Oliver is insecure within himself and is seeking external validation through a need to impress others.
The Duchess and The Jeweller is a short story by Virginia Woolf who recognizes the often conceited and pretentious upper classes and the plight of many within the British working classes. She is equally contemptuous of the jeweller's pretence and his efforts to mix in those circles purely in an effort to reflect his success.
The old woman in the picture is Oliver Bacon's late mother who worried that her son " who began life in a filthy little alley" would not rise above his circumstances. He promised his mother, however and "won my bet" and can now claim to be the "richest jeweller in England." He does recognize that what his mother wanted for him was happiness, as he attempts to apologize for paying the duchess twenty thousand pounds for pearls he was certain were fake, purely for a chance to spend a "long weekend" in the company of the wealthy, in particular, the duchess's daughter.
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